It was a chance encounter. So many things might have prevented it. Had I caught an earlier ferry, or a later train, had we not been following the same route through Greece and Italy, we might never have met.

We noticed each other long before we actually spoke. It was on a shabby Greek train from Athens to the port town of Patras. The carriage was full of Greek soldiers, old women and cigarette smoke.

Outside, the parched countryside sped by. I remembered that Sherlock Holmes was able to calculate the speed of his train by timing the intervals between telegraph poles along the line. I tried, but soon gave up.

“We’re playing cards. Would you like to join?” It was the woman I had noticed earlier, a tall, blonde woman of about 25 years old. She was tanned and moved well and easily. Californian, I thought.

Ethan Hawke and Julie Delphy in the train-board romance, Before Sunrise.

I joined her and her friend, who was small, dark and less attractive than she was. I felt sympathy for this friend, travelling in the shadow of her prettier companion.

Perhaps that is how she had spent her years from high school onwards, the devoted though less noticeable friend, a dark moon moving in the orbit of a brighter planet.

We fell into easy conversation. The blonde woman was about to qualify as a doctor, and was getting married in a few weeks. She decided to “do” Europe before settling down. It was a last breath of freedom.

Her dark friend was to be her bridesmaid. They had been friends since their schooldays. She herself did not make it to college; she worked in a drugstore back home.

Cary Grant and Eve Marie Saint get acquainted in the dining car in North by Northwest.

“So where is home?” I asked. “Sacramento, California,” they replied in unison, and laughed at the coincidence.

I explained that I had been inter-railing through Europe and was now heading home via Brindisi, Venice and Paris. “That’s crazy,” said the blonde, “we’re going the same way. Not Paris, but through Italy to Venice. Why don’t we travel together?”

So we did. By ferry from Patras to Brindisi, and then a long night train journey the length of Italy to Venice. “Get a night train into Venice, stay a day there, and get a night train out. That’s what the guide books say,” said the friend, tapping her copy of “Europe on $25 A Day”.

Over the course of that few days, I got a lesson in the effects of beauty on functionaries in three countries. Railway porters and guards, ticket collectors and waiters all tried a little harder, smiled a little wider and flirted a little more ardently with my blonde American friend.

Charters and Caldicott catch up on the Test match in their carriage in The Lady Vanishes.

The dark companion and I basked in the reflected light, and became brighter and more animated ourselves as a result. This, I remember thinking, it what travel is all about: chance encounters, glamour, the meeting of different cultures and the tantalising promise of romance.

It was, I thought, the kind of thing that can happen only on a train. The rhythm of the movement, the long journeys spent in close proximity to other passengers, the enforced intimacy all combine to make the train a sealed world where anything can happen.

I thought of Cary Grant and Eva Marie Saint thrown together on the 20th Century Limited train from New York to Chicago in Hitchcock’s North by Northwest, or Julie Delphy and Ethan Hawke talking the miles away on a train from Budapest to Vienna in Before Sunrise.

The Santa Lucia train station in Venice.

The train can be a metaphor for a country, too: in The Lady Vanishes, the train becomes a symbol of British values under attack from unspeakable types from eastern Europe. Thank goodness Caldicott and Charters were on board to save the day.

The romance and excitement of train travel can affect all sorts of travellers. The tragic Amanda Knox, now awaiting retrial for the murder of her roommate in Perugia, writes in her book that her first sexual encounter after she came to Europe was on an Italian train.

If there was an unspoken wish for something to happen, it remained unacted upon.

Not that anything like that happened on my journey through southern Europe with my two American friends. The blonde woman often described her trip as a last taste of freedom before marriage. If there was an unspoken wish for something to happen, it remained unacted upon.

We said goodbye on a vaporetto in Venice. They were getting out at the Guggenheim Museum, and I was going on to the train station. They waved until the boat rounded the entrance to the Canale di Santa Maria Maggiore.

We stayed in touch for a while, writing and sending cards. She sent me a photo of her wedding. She looked lovely, and there to her side and slightly behind her stood her dark friend.